Theorems · Theorem · order theory
Set.mem_insert_of_mem
∀ {α : Type u_1} {x : α} {s : Set α} (y : α), x ∈ s → x ∈ insert y s- Defined in
- Mathlib.Data.Set.Insert
- Cited by
- 50 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
Cited by50
Results whose statement or proof uses this declaration.
- right_mem_affineSpan_pairproof · cited by 12
- fg_adjoin_of_finiteproof · cited by 9
- IsOpen.analyticOn_iff_analyticOnNhdproof · cited by 5
- Ideal.map_jacobson_of_surjectiveproof · cited by 4
- HasFPowerSeriesWithinAt.mono_of_mem_nhdsWithinproof · cited by 3
- Vitali.exists_disjoint_subfamily_covering_enlargementproof · cited by 3
- StandardEtalePair.aeval_X_g_mul_mk_Xproof · cited by 3
- Matroid.Indep.closure_sInter_eq_biInter_closure_of_forall_subsetproof · cited by 3
- AffineSubspace.mem_affineSpan_insert_iffproof · cited by 3
- IntermediateField.Lifts.le_unionproof · cited by 3
- IsPreconnected.biUnion_of_reflTransGenproof · cited by 3